关键词： 68C25  

摘要： In this paper we obtain an effective algorithm for quantifier elimination over algebraically closed fields: For every effective infinite integral domain k, closed under the extraction of pth roots when the characteristic p of k is positive, and every prenex formula phi with r blocks of quantifiers involving s polynomials F-1,...,F-s is an element of k[X-1,...,X-n] encoded in dense form, there exists a well-parallelizable algorithm without divisions whose output is a quantifier-free formula equivalent to phi. The sequential complexity of this algorithm is bounded by O(\phi\) + D-(O(n)r), where \phi\ is the length of phi and D greater than or equal to n is an upper bound for 1 + Sigma(i=1)(s) degF(i), and the polynomials in the output are encoded by means of a straight line program. The complexity bound obtained is better than the bounds of the known elimination algorithms, which are of the type \phi\.D-ncr, where c greater than or equal to 2 is a constant. This becomes notorious when r = 1 (i.e., when there is only one block of quantifiers): the complexity bounds known up to now are not less than D-n2, while our bound is D-O(n). Moreover, in the particular case that there is only one block of existential quantifiers and the input polynomials are given by a straight line program, we construct an elimination algorithm with even better bounds which depend on the length of this straight line program: Given a formula of the type There Exists x(n - m + 1,...,) There Exists x(n): F-1(x(1),...,x(n)) = 0 boolean AND ... boolean AND F-s(x(1),...x(n)) = 0 boolean AND G(1) (x(1),..., x(n)) not equal 0 boolean AND ... boolean AND G(s') (x(1),..., x(n)) not equal 0 where F-1,..., F-s is an element of k[X-1,...,X-n] are polynomials whose degrees in the m variables Xn - m + 1,...,X-n are bounded by an integer d greater than or equal to m and G(1),...,G(s') is an element of k[X-1,...,X-n] are polynomials whose degrees in the same variables are bounded by an integer delta, this algori

关键词： MACHINE-tools   FUZZY mathematics  

摘要： The accuracy and precision of CNC machine tools directly affect the quality of machined parts. Automatic diagnosis of faults can improve the maintenance efficiency of CNC machine tools, and thus increase production uptime and improve product quality. In this study, the typical fault categories of CNC machine tools, such as cyclic, backlash, scale mismatch, etc., are taken as reference patterns and recognized by the fuzzy mathematics algorithm with the machine contouring trajectory measured by an inspection device. A primary component extraction (PCE) method is introduced to recognize multiple-cause faults. The study shows that the fuzzy pattern recognition method is able to identify major components of machine tool faults, their categories and direction simultaneously, with a small amount of sampling data. As a feature-based method of fault diagnosis, the PCE method can be integrated into the computer-aided maintenance of manufacturing systems.

摘要： The article reviews the results on algebraic foundations of the applied theory of algorithms, so-called algorithmics, which stems from systems of algorithmic algebras (SAA) [1] and is intensively studied by Glushkov's Ukrainian algebraic-cybernetic school. The object of study in algorithmics includes models of algorithms and programs represented by schemes. The method of algorithmics relies on the apparatus of computer algebra and logic and is intended for the construction of applied problem-solving algorithms. In this way it differs from the classical theory of algorithms, which deals with algorithmic systems such as normal algorithms, computable functions, Turing machines, etc. [2]. Section 1 examines the expressive power of SAA and their modifications. The topic of functional completeness for the metaalgebras of algorithmics associated with various algorithm and program design methods is discussed in Section 2. Section 3 describes some applications of the apparatus of the algebra of algorithmics. In conclusion we suggest some problems whose solution may be a next step for further research in this area of computer science.

关键词： 阴极保护   边界元法   柱面单元   分段线性拟合  

摘要： 用边界元法(BEM)求解区域性阴极保护的数学模型,以往采用矩形单元离散,步骤比较复杂,工作量大。当被保护体的几何形状适宜进行柱面单元划分且同一柱面单元截口线上的电位可视为近似相同时,采用柱面单元离散,可减少模型中节点的数量,缩短计算周期。利用可变误差多面体寻忧时,以往对阴极极化曲线的拟合过于简单,寻优的平稳性较差。对阴极极化曲线进行分段线性拟合,可使寻优过程更加平稳。按上述方法编制的程序BEMU已用于油井套管外加电流阴极保护系统的工程设计。

关键词： 二值图象编码   形态学   膨胀   腐蚀  

摘要： 本文利用图象的几何特征，提出了一种二值图象无失真快速编码算法。用数学形态学技术来提取图象的轮廓信息，给出了输入图象被结构元素膨胀和腐蚀操作的快速算法，并且提出了一种新的轮廓信息编码方法。实验结果表明本文算法非常有效。

关键词： 遗传算法   模式定理   随机搜索  

摘要： 本文介绍了遗传算法的数学基础，遗传算法的特点以及遗传算法和传统优化算法的区别。

关键词： 估算法   正四面体   等比数列   近似计算   直平行六面体   数学素质   全国高考   数学选择题   试题评价   实数根  

摘要： 国家教委考试中心全国高考试题评价组在《1996年全国高考数学试卷评价报告》中有这一样段话:“许多选择题都有一定的运算量,需要进行一些运算方能作出正确的选择。

关键词： Genetic algorithms   Image reconstruction   Reconstruction algorithms   Tomography  

摘要： Combined use of the algebraic reconstruction technique (ART) and the genetic algorithm (GA) shows highly accurate and efficient tomographic reconstruction of line-of-sight projection images of two-phase flows compared with reconstructions obtained by separate use of these methods. A modified GA-based tomography uses the ART reconstruction result as preliminary information on the number. shapes, and sizes of bubbles to be? reconstructed. This combined use of the two methods exploits faster convergence of the ART to the approximate solution space and more robust and accurate optimization of the GA to the ultimate solution space. In the investigation a computer-synthesized phantom field that consisted of five elliptical gas bubbles in liquid or solid surroundings was used. (C) 1998 Optical Society of America.

关键词： project scheduling   branch-and-bound methods   networks/graphs   lower bounds  

摘要： In this paper we consider the Project Scheduling Problem with resource constraints, where the objective is to minimize the project makespan. We present a new 0-1 linear programming formulation of the problem that requires an exponential number of variables, corresponding to all feasible subsets of activities that can be simultaneously executed without violating resource or precedence constraints. Different relaxations of the above formulation are used to derive new lower bounds, which dominate the value of the longest path on the precedence graph and are tighter than the bound proposed by Stinson et al. (1978). A tree search algorithm, based on the above formulation, that uses new lower bounds and dominance criteria is also presented. Computational results indicate that the exact algorithm can solve hard instances that cannot be solved by the best algorithms reported in the literature.

关键词： 人工神经网络   系统辨识   BP网络  

摘要： 在人工神经网络理论中，BP网络是一个重要的人工神经网络，它在非线性分类和高维非线性映射等方面都有着广泛的应用。本文从系统辨识理论入手，既清晰又通俗地阐明了BP算法的数学原理；不失为了解人工神经网络基础理论及加强其它学科理论与人工神经网络理论相互联系的好方法。